A relaxation result for state constrained delay differential inclusions

In this paper, we extend the celebrated Filippov's theorem to delay differential inclusion in n-dimensional real space. We further generalize this theorem to the case when the state variable is constrained to the closure of an open subset. Under a new "inward pointing condition" , we give a relaxation result stating that the set of trajectories lying in the interior of the state constraint is dense in the set of constrained trajectories of the convexified inclusion